In Batch Normalisation, are $\hat{\mu}$, $\hat{\sigma}$ the mean and stdev of the original mini-batch or of the input into the current layer?
Your intuition is correct. We will be normalizing the inputs of the layer under consideration (just right before applying the activation function). 

So, if this layer receives an input $\mathrm{x}=\left(x^{(1)} \ldots x^{(d)}\right)$, the formula for normalizing the $k^{th}$ dimension of $\mathrm{x}$ would look as follows:
$$\widehat{x}^{(k)}=\frac{x^{(k)}-\mathrm{E}\left[x^{(k)}\right]}{\sqrt{\operatorname{Var}\left[x^{(k)}\right]}}$$

Note that in practice a constant $\epsilon$ is also added under the square root in the denominator to ensure stability. 

Source: The original Batch Normalization paper (Section 3). 

Andrew Ng's video on this topic might also be useful for illustration.